Problem #$8$: $($a$)$ Given the initial value problem

$y^{\text{'}}+8y=65sint,y(0)=3,$

find the Laplace transform of the solution $Y(s).$

$($b$)$ Using the Laplace transform, $Y(s),$ find $y(t),$ the solution to our initial value problem.

$*$Don$\text{'}$t forget: Your answer should be a function of $t.$

$($D$)\frac{4}{s+8}-\frac{s-8}{s^2+1}$

$($E$)3+\frac{1}{s+8}-\frac{s-8}{s^2+1}$